Are the new iPod nano and Apple TV running iOS?

Apple introduced a new iPod nano this week with a multitouch screen, and a new Apple TV with an A4 chipset, but didn't make clear if either or both were running iOS. Unlike iPhone, iPod touch, and iPad, where they shout iOS from the rooftops, they've historically kept mum about iPod and Apple TV OS.

iPod nano looks like it's running iOS. It has an iOS-like user interface with a subset of iOS-like built-in apps controlled by iOS-like gestures. There's inertial scrolling with elasticity. You can even put icons into jiggly mode and rearrange them. In fact, when demonstrating that during his keynote, Steve Jobs said (emphasis mine):

Say I that on the home page, I can just push down, jiggle it, and move it, just like I can with my other iOS devices

Not official confirmation to be sure, but think about it this way: given their focus on iOS of late, would Apple spend the effort to re-create that interface on the old iPod OS just for iPod nano, or to spend it getting iOS running on iPod nano hardware?

Apple TV on the other hand looks nothing like iOS. However, it's running on an Apple A4 chipset which has, thus far, only been used for iOS devices. Again, given Apple's focus on iOS, would they spend the effort porting OS X to Apple A4 just for Apple TV, or recreate the Apple TV UI for iOS?

I didn't hear Jobs mention anything about iOS during the show but Daring Fireball's John Gruber claims it's definitely iOS.

I'd love to know for sure, but for now my guess is Apple sees iOS as their future and any effort they put in to new mobile or media devices is going to be put into iOS, including iPod nano and Apple TV.